Odd how the stories always grow and change to insulate themselves from the cruel lens of reality.
We all want certainty in an ambiguous world. When someone said it occurred "During" the debates, that could describe the entire period of time between when they started the first debate, till after they went home from the last one, depending on how the original claimant regarded their use of the term "during." That confusion could creep in to the English language due to a lack of precision is not note worthy.
At this point, (noting the comment from Obama about being Minister of Illinois) the worst case scenario is that something has been misheard or misunderstood and repeated/amplified by the internet. This establishes that there is at least a small kernel of truth to the origin of this meme.